Understanding Landau Levels for 3D Fermionic Gas in Magnetic Field

[Sunny Singh]

TL;DR Summary

Need an explanation of dimensionality reduction in this case.

I am a beginning graduate student and I've been assigned a paper which uses landau levels for 3d fermionic gas in uniform background magnetic field. I am having trouble finding a proper source which deals with solution of dirac equation in such a case. With the two papers that i have found which talks about it, i am finding it difficult to understand the degeneracy of landau levels and the associated density of states when it comes to finding the integration measure. Can you please suggest me a source, either in a book or any research article which explains landau levels for 3d fermions in detail?

 

[vanhees71]

Which two papers have you read? Aren't there references to other papers or even textbooks?

 

[Sunny Singh]

Which two papers have you read? Aren't there references to other papers or even textbooks?

This is the first one: https://arxiv.org/abs/0705.4275
and the second one: https://arxiv.org/abs/1812.08886The one book that i found which deals with this problem is: Quantum Electrodynamics by Akhiezer and Berestetskii.

But given that the problem statement seems so simple i thought this must have been dealt with in many more books or papers but even though some books have a paragraph or two on this, none of them discuss the structure of landau levels and density of states in the direction perpendicular to the Pz motion (constant B in z direction) except the book i mentioned above. I was hoping that someone here would have experience with the structure of landau levels in case of 3d fermions since most of landau level stuff online is on electrons confined in 2 dimensions in the context of solid state physics.

 

[MathematicalPhysicist]

There's a relatively new book by Fuxiang Han which you can look at amazon.

I bought the problem book, while I needed also to buy the main text.
I am not sure it covers Landau levels of 3d fermions, but you can give it a look if your library has a copy.

 

[Sunny Singh]

There's a relatively new book by Fuxiang Han which you can look at amazon.

I bought the problem book, while I needed also to buy the main text.
I am not sure it covers Landau levels of 3d fermions, but you can give it a look if your library has a copy.

Thanks, i'll look into it.